When you say you replaced the rear end, was it just the ring and pinion or the entire rear end axel assembly. The wearing of the tires on the inside only seems to indicate a mismatch replacement of the rear end or improper installation. Obviously the wear on the tires indicate an alignment issue. Which would also cause the swaying of the rear end.

YOU DIDN'T SAY IF YOU HAVE MAGS OR NOT ON THE MUSTANG, BUT TOM COULD JUST BE RIGHT. IF YOU DO HAVE MAGS, MAKE SURE YOU DON'T STILL HAVE THE STOCK LUG BOLTS. IF THEY ARE STOCK THEY ARE NOT LONG ENOUGH TO COMPENSATE FOR THE EXTRA THICKNESS OF THE MAGS, GIVING YOU LOOSE LUG NUTS.